Question: Simplify. Remove all perfect squares from inside the square roots. Assume $a$ and $b$ are positive. $\sqrt{81a^5b}=$
Explanation: $\begin{aligned} \sqrt{81a^5b}&=\sqrt{9^2 \cdot \left( a^2\right)^2\cdot ab} \\\\ &=\sqrt{9^2}\cdot\sqrt{\left( a^2\right)^2}\cdot\sqrt{ab} \\\\ &=9\cdot a^2\cdot\sqrt{ab} \\\\ &=9a^2\sqrt{ab} \end{aligned}$ In conclusion, $\sqrt{81a^5b}=9a^2\sqrt{ab}$